Sadonkorjuu

import java.util.ArrayList;
import java.util.LinkedList;
import java.util.Scanner;

public class Cities2 {
    public static void main(String[] args) {
        Scanner input = new Scanner(System.in);
        int cityCount = Integer.parseInt(input.nextLine());
        City[] cities = new City[cityCount];
        ArrayList<City> cursors = new ArrayList<>();

        // Cities
        int i = 0;
        for (String s : input.nextLine().split(" ")) {
            boolean isField = s.equals("1");
            City city = new City(isField);
            cities[i++] = city;
            if (!isField) cursors.add(city);
        }

        // Routes
        for (int linei = 1; linei < cityCount; linei++) {
            String[] line = input.nextLine().split(" ");

            City from = cities[Integer.parseInt(line[0]) - 1];
            City to = cities[Integer.parseInt(line[1]) - 1];
            int length = Integer.parseInt(line[2]);

            from.routes.add(new Route(to, length));
            to.routes.add(new Route(from, length));
        }

        // Actual stuff starts here.
        long totalLength = 0;
        while (!cursors.isEmpty()) {
            ArrayList<City> nextCursors = new ArrayList<>();
            for (City city : cursors) {
                for (Route route : city.routes) {
                    City destination = route.destination;
                    int newLength = city.shortestRoute + route.length;
                    if (newLength < destination.shortestRoute) {
                        totalLength = totalLength - (destination.shortestRoute == Integer.MAX_VALUE ? 0 : destination.shortestRoute) + newLength;
                        destination.shortestRoute = newLength;
                        if (destination.routes.size() > 1) nextCursors.add(destination);
                    }
                    destination.routes.remove(route);
                }
            }
            cursors = nextCursors;
        }

        System.out.println(totalLength);
    }

    public static class City {
        public LinkedList<Route> routes = new LinkedList<>();
        public int shortestRoute = Integer.MAX_VALUE;

        public City(boolean isField) {
            if (!isField) shortestRoute = 0;
        }
    }

    public static class Route {
        public City destination;
        public int length;

        public Route(City destination, int length) {
            this.destination = destination;
            this.length = length;
        }
    }
}

Test 1

Group: 1, 2

Verdict: ACCEPTED

Test 2

Group: 1, 2

Verdict: ACCEPTED

Test 3

Group: 1, 2

Verdict: ACCEPTED

Test 4

Group: 1, 2

Verdict: ACCEPTED

Test 5

Group: 1, 2

Verdict: ACCEPTED

Test 6

Group: 1, 2

Verdict: ACCEPTED

Test 7

Group: 2

Verdict: TIME LIMIT EXCEEDED

Test 8

Group: 1, 2

Verdict: ACCEPTED

Test 9

Group: 2

Verdict: TIME LIMIT EXCEEDED

Test 10

Group: 1, 2

Verdict: ACCEPTED

Test 11

Group: 2

Verdict: TIME LIMIT EXCEEDED

Test 12

Group: 2

Verdict: TIME LIMIT EXCEEDED

Test 13

Group: 2

Verdict: TIME LIMIT EXCEEDED

Test 14

Group: 2

Verdict: TIME LIMIT EXCEEDED

Test 15

Group: 1, 2

Verdict: ACCEPTED

Test 16

Group: 1, 2

Verdict: ACCEPTED

Test 17

Group: 1, 2

Verdict: ACCEPTED

Test 18

Group: 1, 2

Verdict: ACCEPTED

Test 19

Group: 1, 2

Verdict: ACCEPTED

Test 20

Group: 1, 2

Verdict: ACCEPTED

Test 21

Group: 2

Verdict: TIME LIMIT EXCEEDED

Test 22

Group: 2

Verdict: TIME LIMIT EXCEEDED

Test 23

Group: 2

Verdict: TIME LIMIT EXCEEDED

Test 24

Group: 1, 2

Verdict: ACCEPTED

Test 25

Group: 2

Verdict: TIME LIMIT EXCEEDED

Test 26

Group: 1, 2

Verdict: ACCEPTED

Test 27

Group: 2

Verdict: TIME LIMIT EXCEEDED

Test 28

Group: 1, 2

Verdict: ACCEPTED

Test 29

Group: 2

Verdict: TIME LIMIT EXCEEDED

Test 30

Group: 1, 2

Verdict: ACCEPTED

Test 31

Group: 2

Verdict: TIME LIMIT EXCEEDED